This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Dennis, hebu tusuluhishe hili. Tunapewa x = (1)/(sqrt(5)) na x ni pembe kali. a) (i) Tafuta x Step 1: Tumia utambulisho wa Pythagorean ^2 x + ^2 x = 1. Badilisha thamani ya x: ((1)/(sqrt(5)))^2 + ^2 x = 1 (1)/(5) + ^2 x = 1 Step 2: Tatua kwa ^2 x. ^2 x = 1 - (1)/(5) ^2 x = (4)/(5) Step 3: Tafuta x. Kwa kuwa x ni pembe kali, x itakuwa chanya. x = sqrt((4)/(5)) x = (2)/(sqrt(5)) Ili kurahisisha, zidisha nambari na denominata kwa sqrt(5): x = 2sqrt(5)5 Jibu la (i) ni 2sqrt(5)5. a) (ii) Tafuta ^2 (90^ - x) Step 1: Tumia utambulisho wa kikoa (90^ - x) = x. Hivyo, ^2 (90^ - x) = ( x)^2. Step 2: Badilisha thamani ya x. ^2 (90^ - x) = ((1)/(sqrt(5)))^2 ^2 (90^ - x) = (1)/(5) Jibu la (ii) ni (1)/(5). a) (iii) Tafuta 2x Step 1: Kwanza, tafuta x. Tunajua x = ( x)/( x). x = (1)/(sqrt(5))(2)/(sqrt(5)) x = (1)/(2) Step 2: Tumia fomula ya 2x: 2x = (2 x)/(1 - ^2 x). Badilisha thamani ya x: 2x = (2 (1)/(2))1 - ((1)/(2))^2 2x = (1)/(1 - 1)4 2x = (1)/(3)4 2x = (4)/(3) Step 3: Tafuta 2x. Tunajua 2x = (1)/( 2x). 2x = (1)/(4)3 2x = (3)/(4) Jibu la (iii) ni (3)/(4). That's 2 down. 3 left today — send the next one.